A B767-200 FLT IS GIVEN A CLRNC MEANT FOR ANOTHER FLT WITH A SIMILAR SOUNDING CALL SIGN BY CTLR AT ZDC; DC.

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AT FL280 OVER GVE WE HEARD ZDC ATC CLRNC 'FLT IE; EXPECT MAYAS AT FL220; DSND AND MAINTAIN FL240.' I (THE FO) READ BACK CLRNC 'FLT IE WE'LL EXPECT THAT; LEAVING FL280 FOR FL240.' THERE WAS NO FURTHER XMISSION FROM ZDC. PER COMPANY PROC I PLACED FL240 IN ALT WINDOW; POINTED TO IT AND CALLED FL240. THE CAPT CONFIRMED CLRNC; HE POINTED TO ALT WINDOW AND CALLED FL240. AFTER DSCNT BEGAN; ZDC CALLED BACK AND ASKED OUR ALT. I ANSWERED 'DSNDING OUT OF FL265 FOR FL240.' ATC THEN SAID 'I DID NOT GIVE YOU A DSCNT CLRNC.' I ANSWERED 'YOU GAVE US EXPECT MAYAS AT FL220; DSND TO FL240. I READ IT BACK AS FLT IE; WHAT ALT DO YOU WANT?' THE CTLR SAID 'MAINTAIN FL260 NOW.' LATER HE CAME BACK AND SAID THAT CLRNC WAS FOR FLT HIE. HOWEVER; I (THE FO); THE CAPT AND IRO ALL HEARD THE CLRNC AS FOR FLT IE. THE CTLR NEVER ANSWERED OR CHALLENGED MY READBACK. ALSO; FLT HIE DID NOT CHALLENGE ME AS READING BACK HIS CLRNC. IN 30 YRS OF FLYING; THIS IS A FIRST FOR ME AND A VERY DISTURBING INCIDENT. THANKFULLY THERE WAS NO TFC CONFLICT. I CAN SEE 3 SCENARIOS THAT RESULTED IN THIS INCIDENT: 1) ALL 3 OF US IN COCKPIT HEARD CLRNC AS FOR IE INCORRECTLY. 2) THE CTLR ACCIDENTALLY READ BACK CLRNC AS FOR IE. 3) POSSIBLY THERE WAS BLOCKED XMISSIONS. SUPPLEMENTAL INFO FROM ACN 487777: A POSSIBILITY COULD BE THAT HIE AND IE (US) READ THE CLRNC AT EXACTLY THE SAME TIME AND THE CTLR ONLY HEARD THE IE PORTION.